B.2. Abbreviating Binary Numbers as Octal and Hexadecimal Numbers
The main use for octal and hexadecimal numbers in computing is for abbreviating lengthy binary representations. Fig. B.7 highlights the fact that lengthy binary numbers can be expressed concisely in number systems with higher bases than the binary number system.
Decimal number | Binary resentation | Octal resentation | Hexadecimal resentation |
---|---|---|---|
0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 |
2 | 10 | 2 | 2 |
3 | 11 | 3 | 3 |
4 | 100 | 4 | 4 |
5 | 101 | 5 | 5 |
6 | 110 | 6 | 6 |
7 | 111 | 7 | 7 |
8 | 1000 | 10 | 8 |
9 | 1001 | 11 | 9 |
10 | 1010 | 12 | A |
11 | 1011 | 13 | B |
12 | 1100 | 14 | C |
13 | 1101 | 15 | D |
14 | 1110 | 16 | E |
15 | 1111 | 17 | F |
16 | 10000 | 20 | 10 |
A particularly important relationship that both the octal number system and the hexadecimal number system have to the binary system is that the bases of octal and ...
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